972Unsolved Historical Ciphers
93 32 13 19 22 16 63 02 11 63 14 24 69 44 72 71 94 24
il n y a pas e u de p u i s l on g te m s
5, 8 = nulls · 24 = s · 29 = t · 62 = que · 46 = qui · 66 = pour · S./. = in clear

The Hague → Dresden · two-figure letter-and-syllable cipher, unseparated, with nulls · December 1754 – May 1756

Johann Heinrich Kauderbach’s intercepted despatches from The Hague, 1754–56

Koninklijk Huisarchief, The Hague, Prins Willem V inv. 201: the Dutch copies of ten letters in which the Saxon-Polish resident Johann Heinrich Kauderbach put his secret passages in figures (DECODE R1043, R1044, R1954, R1958, R1959, R2078–R2082). DECODE records that the Dutch cabinet could not decipher them; no later decipherment was found in print or on DECODE.

The nulls were identified and the figures divided into two-figure codes. The key was then recovered from the ciphertext alone, by a solver that assigned the codes to the letters and syllables of Kauderbach’s 1761 key in Dresden. All ten letters are decrypted, 65–97% of the cipher per letter.

Daniel Bourdeau · posted · updated

Method: key recovered from ciphertext-only · Extent: complete

Summary. The Dutch opened and copied the letters of the Saxon resident at The Hague, and ten of the copies carry passages in figures. DECODE notes that the Stadtholder’s cabinet deciphered none of them: Kauderbach wrote the figures without any separation, so that the Stadtholder’s office could not even tell where one group ended and the next began. Here the division into groups was recovered first. The digits 5 and 8 never occur inside a group and are nulls; with them removed the stream falls into two-figure groups (first figure 0–4, 6, 7 or 9, second 1–4, 6, 7 or 9), about sixty of them, one key for all four years. A homophonic solver found nothing. The way in was Kauderbach’s own cipher of 1761, kept in Dresden and imaged on DECODE (R936): two-figure numbers for letters and syllables (ai, de, en, que, qui, pour…), capitals for names, and a declared null. Its numbers do not fit the 1754 letters, but its vocabulary does. An annealing search for a one-to-one assignment of the 1754 codes onto it converged twice to the same key from different starts, and hand correction fixed the rest (01 = oi, 12 = ai, 27 = in, 66 = pour). In each letter 65–97% of the cipher now decrypts to sense. They cover the Dutch argument over the thirty-thousand-man augmentation in 1755, Colonel Yorke and the renewal of the Saxon subsidy treaty, and the news of the Treaty of Versailles of May 1756 (“une consternation extraordinaire ici”). The names stay in clear capitals (S./., Q./., P./.), whose 1754 meanings are known only from context.
Head of the intercept copy of Kauderbach's letter of 23 December 1754: clear French, then unseparated figures
DECODE R2078, the copy of Kauderbach’s letter of 23 December 1754, first page: Les Etats de Holl. se separeront enfin samedi jusqu’à nouvelle convocation, then the figures, 9332131922166302… = il n’y a pas eu depuis longtems…; the margin note reads Details relatifs a la Commission du Cte d’Affry auprès de cet Etat. Image: Koninklijk Huisarchief, The Hague, Archief Prins Willem V inv. 201, via DECODE R2078.

01 The documents

Kauderbach (1707–1785) served the Saxon legation at The Hague from 1739 for almost thirty years; his despatches went to Count Brühl in Dresden (“Votre Excellence”). The Dutch post office copied them for the Stadtholder’s cabinet, and the copies are in the Koninklijk Huisarchief, Prins Willem V inv. 201, beside the d’Affry intercepts of inv. 192. Most are wholly in clear. DECODE catalogued the ten with figures, from photographs, and transcribed three.

DECODEDatePagesCipher groupsTranscription
R207823 Dec 175451,231DECODE
R195820 Jun 17552542this project
R20796 Jul 17552558this project
R208022 Jul 175541,260this project
R19595 Aug 17552391this project
R208112 Aug 17553802this project
R208215 Aug 17552425this project
R104429 Sep 17553628DECODE
R195416 Mar 175641,621this project (weak)
R104325 May 175651,054DECODE

DECODE dates R1959 to 5 August 1758; its heading reads 5 Aout 1755, and its content (the rumoured negotiation of Prussia, the Staroste of Warsaw leaving for London) belongs to that summer. Group counts are after removing nulls, measured on cipher/R*.txt: 8,512 groups in all. R1954 is a photocopy in a different hand, with letter-like figures; its transcription infers many digits from the pair rules and is the weakest.

02 Splitting the figures

The Hague cabinet’s note on DECODE gives the reason for their failure: “the codegroups are not separated, by blanks or dots as is usually the case.” A first count showed no preferred period of two or three figures from the start of a passage, and the copyists’ spacing is not systematic. Two figures behave differently from the rest. 5 and 8 are rare (135 and 78 in the first 6,096 digits), never follow 5 or 8, and typically stand next to the clear sigla (…254 M./., J./. C./. 8095…). Deleting them as single figures restores a clean two-figure phase (index of coincidence 0.027 against 0.021 for the shifted reading; for four-figure windows 0.155 and 0.161 at offsets 0 and 2, 0.103 at 1 and 3). A short Viterbi pass over the pair frequencies then repairs the places where a copyist dropped or doubled a figure. What is left is a table of about sixty two-figure groups: first figure 0, 1, 2, 3, 4, 6, 7 or 9, second 1, 2, 3, 4, 6, 7 or 9, never 0, 5 or 8. Every letter shows the same frequency profile, so one key served from 1754 to 1756 at least.

A homophonic solver failed on that table. A hill-climbing solver that decrypts synthetic French in the same form (sixty codes, two per cent noise, nulls, realignment) at 98% produced nothing on the real stream, in French, German, Dutch or Italian, with nulls or merged look-alike figures. The statistics of the stream still looked like language (entropy, vowel alternation 0.63, long exact repeats such as 19 29 14 44 nineteen times), so the units were not single letters.

03 The key

Kauderbach's 1761 cipher: for enciphering and deciphering, two-figure numbers for letters and syllables, capitals for names
Hauptstaatsarchiv Dresden 10024 Loc. 08236/11 Bl. 5, the cipher for “Kauderbach in Den Haag”, 1761 (DECODE R936): pour chiffrer and pour déchiffrer, one number for each letter or syllable, the capitals A–Z for persons and states (S la Hollande, T l’Angleterre, U France), and 6. est faux chiffre. DECODE’s transcription has “30 ni?” for 30 m. Image: Sächsisches Hauptstaatsarchiv Dresden, 10024 Geheimer Rat, Loc. 08236/11 Bl. 5, via DECODE R936.

DECODE also holds the Dresden chancery’s cipher register, and one of its leaves is the key made for Kauderbach in 1761. It explains the 1754 system at once: a null figure, capitals in clear for the names, and a single number for each of about seventy letters and syllables. It is not the same key (its numbers use 5 and 8), but a successor of the same design. So the problem became an assignment: each 1754 code to a different item of the 1761 vocabulary. A simulated-annealing search over such assignments, scored by a four-letter French model built from contemporary diplomatic letters, reached the same key from two independent starts (seeds 22 and 24, −3.85 per letter, against −3.95 for true French on the same model), and the result was French. Reading the decryption then settled what the 1761 vocabulary lacked or the search had misplaced: 27 in (principales, provinces, interet), 91 ou, 33 qu, 79 st, 17 par, 22 pas, 46 qui, 66 pour, 23 fai, 76 ke (Yorke, Kniphausen), 77 z (treize, declarez), and the exchange of 01 oi and 12 ai, found independently by both readers (avoit, etoit, croire; raisons, mais, Pais Bas).

01 oi · 02 de · 03 re · 04 au · 06 ie · 07 le · 09 ne · 10 z? · 11 p · 12 ai · 13 y (re) · 14 i · 16 e · 17 par · 19 a · 20 fe? · 21 ce · 22 pas · 23 fai · 24 s · 26 et · 27 in · 29 t · 30 an · 31 b · 32 n · 33 qu · 34 du · 36 si · 37 en · 39 pr · 40 em? · 41 la · 42 ra · 43 c · 44 on · 46 qui · 47 f · 49 sa · 60 ent · 61 h · 62 que · 63 u/v · 64 d · 66 pour · 67 se · 69 l · 71 te · 72 g · 73 o · 74 ci · 76 ke · 77 z · 79 st · 90 k? · 91 ou · 92 r · 93 il · 94 m · 96 co · 97 x · 5, 8 nulls

04 The decrypted letters

Word division, accents and the bracketed sigla are editorial; spelling is Kauderbach’s. […] marks an undecrypted stretch, [?] a doubtful word. The clear passages are summarised in brackets.

R2078, 23 December 1754 (about 90%)

[Clear: the Estates of Holland will separate on Saturday until a new convocation.] Il n’y a pas eu depuis longtems une assemblée des etats de Holl. dont les objets de deliberations aient eté plus importans et en meme tems plus embarassans pour cet etat. D’un coté l’ouverture faite par le comte d’Affry presente mille epines, et quant au fond et quant a la forme des conferences a entamer …; de l’autre coté le colonel Yorke, qui ne s’endort pas dans ces circonstances, demande dans un memoire … des explications sur ce a quoi l’on peut se tenir relativement aux engagemens … The overture is to go through commissioners, conferences auxquelles le marquis de Bonnac agira et parlera comme chef de l’ambassade; the opponents of England font assez connaitre que le principal but est de negocier un [traité] de neutralité.

R1958, 20 June 1755 (about 90%)

Le colonel Yorke m’a de nouveau assuré que sa cour est tres disposée au renouvellement du [traité] de subside, et qu’il ne doutoit pas que Mr le comte de Fleming … ne s’affectionnat a cette affaire a son arrivée a Hanovre. Yorke himself, dans des momens d’impatience, se sentoit incliné pour le sisteme des anticontinentistes; Kauderbach thinks Hanover the right place pendant qu’on y est encore dans l’incertitude des evenemens en Amerique.

R2079, 6 July 1755 (about 97%)

Mr Haslang mande au resident de Baviere qu’il a la parole du duc de Newcastle que son [Y./.] sera renouvellé. Les apparences pour l’augmentation des [Z./.] diminuent de jour en jour … mais j’ai de fortes raisons de croire qu’il n’en sera que mieux pour nos affaires: Amsterdam would sooner renew the subsidies than vote an augmentation, qui dans leurs principes en est une pour le pouvoir du stadhouder.

R2080, 22 July 1755 (about 97%)

Les principales raisons qu’on a alleguées dans les debats qu’il y a eu sur ce sujet dans l’assemblée de [S./.] se reduisent en substance aux suivantes. Primo, que si le danger dont les Pays Bas sont menacés est tel que le lord Holderness l’a fait connaitre ici, une augmentation de trente mille hommes n’est pas suffisante pour le detourner. Secundo, qu’il faut constater avant toutes choses si le danger est reel pour la republique … Tertio, Holland cannot carry the burden alone while Zeeland, Utrecht, Friesland and Groningen plead exhaustion; quarto, dans le cas de necessité … tous les bons patriotes devroient sacrifier jusqu’au dernier sol et combattre pro aris et focis; mais qu’il faudroit auparavant s’expliquer avec [Q./.]. If it must be, new taxes and encore un cinquantieme denier.

R1959, 5 August 1755 (about 95%)

Le bruit que [E.M.] est en negociation avec [P.] ne paroit pas etre entierement sans fondement, et l’on assure que l’on a fait reellement quelques demarches aupres de ce prince, qui auroit promis a certaines conditions de se tenir tranquile tant que la [J./. C./.] ne remueroit pas. The ambassador of [Q./.] m’a sondé plusieurs fois sur les dispositions de [J./.] pour un [traité] de subside avec la sienne, a quoi je lui ai repondu constamment que je n’etois pas instruit, et que nous avions un [ministre] a Paris auquel il etoit plus naturel de s’adresser qu’a moi.

R2081, 12 August 1755 (about 93%)

Les [P.] sont aussi peu contens de [J./. C./.] que des [S./.]. Il me paroit qu’ils soupconnent [U./.] de ne vouloir pas elle meme au fond embrasser ces choses … Ils disent savoir positivement que le baron de Kniphausen declame plus fortement a Compiegne contre les [P./.] que [Q./.] meme. The rumoured negotiation with [M./.] is now denied: an attempt was made three months ago mais qu’elle n’a pas pris.

R2082, 15 August 1755 (about 95%)

L’ambassadeur de [Q./.] assure que [E.M./.] a ecrit au roi son maitre une lettre de sa propre main … qu’il avoit une armée de cent cinquante mille hommes a son service. [P./.] says openly that if the Dutch will not arm, [P./.] abandonnera le continent, et qu’elle ne sacrifiera pas … la seule occasion decisive d’humilier [Q./.] a la pitoyable conduite de [S./.], qui apres avoir eté assez avertie se tirera d’affaire comme elle pourra.

R1044, 29 September 1755 (about 85%)

L’on n’entend que des plaintes des membres contre [P.I.] de ce qu’ils font tant de prises en Europe sans en donner aucune raison au public; England had taken pour plus de vingt millions de prises sur les sujets de l’Etat in the last war, qu’on recommençoit deja ce train. [Clear: Bolza’s power useless; Kauderbach’s arrears.]

R1954, 16 March 1756 (about 65%)

On the demand for a secours de six mille hommes: [S./.] ne peut refuser ce secours sans rompre entierement avec [B./.], qui prendra ce refus pour une infraction …; if the neutrality party loses, le peuple s’animera … et entrainera l’Etat malgré lui dans la querelle. Many gaps: the transcription is weak.

R1043, 25 May 1756 (about 85%)

On a aujourd’hui des avis certains et positifs que le [traité] dont on parle depuis si longtems a eté signé a Versailles le deux de ce mois, et selon ce qu’on m’a [fait] conter confidemment, il a pour objet primo la neutralité des Pais Bas, secundo il doit y etre stipulé qu’aucune puissance ne donnera aucun secours a l’ennemi de l’autre … et tertio … de ne pas lui etre contraire relativement a l’election d’un Roi des Romains. Cette nouvelle a causé une consternation extraordinaire ici parce qu’on croit qu’il y a des articles secrets qui vont encore plus loin. Then Bonnac and d’Affry’s visit to an ambassador’s country house, et l’on a dit aussi beaucoup de reflexions sur cette demarche. The First Treaty of Versailles was signed on 1 May 1756.

05 What remains open

06 Sources

Transcriptions, the split code stream, the key, the solver scripts and the full readings are in kauderbach1754/.